Game Theory

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Transcript of Game Theory

Game TheoryThe science of strategyStudies strategic situations: the payoff to a participant in the interaction depends not only on his/her/its own actions, but also on the actions of others.HistorySimultaneous move gamesSequential move gamesRepeated gamesWhat is a game?Players: who are the participants in the interaction?Strategies: what are the choices of the players?Payoffs: what are the consequences of various combinations of choices?AliceBobMumRatMumRat-1-1-5-5-1000-10Prisoner's DilemmaBob10Stay-10Alice10SwerveSwerveStayChicken-10-2-2AliceBattle of the sexesBob30100Game3GameShowShow6010Penalty kickLeftLeftRight1Right10KickerGoalie0061010HEXAliceBobenterstay outfightacquiesce150022fight2Aliceacquiesce20Bob0enter51stay out25fight012enterstay outAlice0Bobacquiesceacquiesce1enterBob020Alice5fight2stay outSubgame perfect equilibriumStart at the end: analyze the endgame first"Roll back" the optimal actions from thereRules out incredible threatsCommitmentHow can you change the game to make your threat credible?Scuttle your shipsReduce your optionsBiblical times: GT in the Bible 1838: Cournot1913: Zermelo: in chess, either white can force a win, or black can force a win, or both sides can force a draw.1928: Von Neumann’s minimax theorem 1944: Von Neumann and Morgenstern 1950-53: Nash 1952: John Charles C. McKinsey, Introduction to the Theory of Games1972: International Journal of Game Theory was founded by Oskar Morgenstern1990: The first graduate level microeconomics textbook to fully integrate game theory into the standard microeconomic material was David M. Krep’s A Course in Microeconomic Theory1994: Nash, Harsanyi, Selten Nobel 2005: Aumann, Schelling Nobel2007: Hurwicz, Maskin, Myerson NobelGT is central to economics, becoming important in political science, bi- ology, psychology, sociology, has applications in philosophy, pure mathematics, business!Mechanism DesignRatMum-10-1-5Mum00-1Bob-10RatAlice-5Prisoner's DilemmaPlay the same game repeatedly Total payoff: Sum or average of stage payoffsOr, the discounted sum of payoffsIn repeated games,Outcomes that are not sustainable in the stage game could be equilibrium outcomesCooperation is much easier to sustainChange the perspective:Instead of analyzing a game with given rules, design the rules to achieve desirable outcomesNot the same as "central planning!"Successful applications: auction design, matching (medical residencies, school choice, course registration)http://www.slate.com/id/2108640/Campaign strategy:Business:http://www.newyorker.com/arts/critics/books/2010/07/26/100726crbo_books_gottliebVoting systems:Basic intro:Adam Galambos, Lawrence UniversityKen Binmore: Game Theory A Very Short Introduction